Related Topics:

Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 3, Lesson 2

Student Outcomes

Students understand properties of area:

- Students understand that the area of a set in the plane is a number greater than or equal to zero that measures the size of the set and not the shape.
- The area of a rectangle is given by the formula length Γ width. The area of a triangle is given by the formula 1/2 base Γ height. A polygonal region is the union of finitely many non-overlapping triangular regions and has area the sum of the areas of the triangles.
- Congruent regions have the same area.
- The area of the union of two regions is the sum of the areas minus the area of the intersection.
- The area of the difference of two regions where one is contained in the other is the difference of the areas.

**Properties of Area**

Classwork

**Exploratory Challenge/Exercises 1β4**

- Two congruent triangles are shown below

a. Calculate the area of each triangle.

b. Circle the transformations that, if applied to the first triangle, would always result in a new triangle with the same area:

Translation Rotation Dilation Reflection

c. Explain your answer to part (b).

- a. Calculate the area of the shaded figure below.

b. Explain how you determined the area of the figure. - Two triangles β³ π΄π΅πΆ and β³ π·πΈπΉ are shown below. The two triangles overlap forming β³ π·πΊπΆ

a. The base of figure π΄π΅πΊπΈπΉ is composed of segments of the following lengths: π΄π· = 4, π·πΆ = 3, and πΆπΉ = 2. Calculate the area of the figure π΄π΅πΊπΈπΉ.

b. Explain how you determined the area of the figure. - A rectangle with dimensions 21.6 Γ 12 has a right triangle with a base 9.6 and a height of 7.2 cut out of the
rectangle.

a. Find the area of the shaded region.

b. Explain how you determined the area of the shaded region.

**Lesson Summary**

**SET (description)**: A set is a well-defined collection of objects called elements or members of the set.

**SUBSET**: A set π΄ is a subset of a set π΅ if every element of π΄ is also an element of π΅. The notation π΄ β π΅ indicates
that the set π΄ is a subset of set π΅.

**UNION**: The union of π΄ and π΅ is the set of all objects that are either elements of π΄ or of π΅, or of both. The union is
denoted π΄ βͺ π΅.

**INTERSECTION**: The intersection of π΄ and π΅ is the set of all objects that are elements of π΄ and also elements of π΅. The
intersection is denoted π΄ β© π΅.

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.